For all-vapor releases across the relief valve, the API Recommended Practice 520 provides the standard sizing equation (in Section 18.104.22.168 of the 6th edition). The flow is a function of the nozzle area, the inlet absolute pressure and temperature, and several fluid properties. In addition to the discharge coefficient (Kd), discussed above, the equation also includes a correction factor (Kb) for the effects of back pressure on the flow through a balanced pressure relief valve. The value for Kb should normally be obtained from the manufacturer. If Kb is not available for a specific valve, the generic curve given in API RP 520 may be used.
The measured values of Kd are a function of the phase of the relief fluid. Therefore, the values discussed above for liquid sizing are not to be used when sizing for gas or vapor flow. Valve manufacturers and the National Board publish separate values of Kd for vapor flow. The same caveats discussed above apply when sizing for vapor flow; the API recommended default value of Kd for vapor flow is 0.975.
The vapor-sizing equation discussed above was derived for the case of critical flow – that is, flow that is independent of the downstream pressure. In the unusual occurrence that the downstream pressure is on the order of 50% of the relief pressure, the vapor flow is in the subcritical regime, and a different equation describes the flow. See API Recommended Practice 520 Part I for further description of critical and subcritical flow regimes. For convenience, API has generated a set of values of Kb as a function of pressure downstream of the pressure relief valve that enable the use of the critical flow equation to calculate the subcritical flow capacity of conventional and pilot-operated valve. Thus, with the inclusion of an additional generic curve for Kb, one equation can suffice for both flow regimes.